# MCP Interface Implementation Plan

## Overview

This document outlines the plan to implement a Model Context Protocol (MCP) interface for the sublinear-time-solver project using the FastMCP TypeScript library. The MCP server will provide structured access to the solver algorithms and enable integration with AI assistants and other tools.

## Goals

1. Create an MCP server that exposes the sublinear-time solver functionality
2. Use FastMCP TypeScript library for rapid development
3. Distribute as an npx-executable package for easy installation
4. Provide both programmatic API and command-line interface

## Technology Stack

- **Language**: TypeScript
- **Framework**: FastMCP
- **Runtime**: Node.js
- **Package Manager**: npm/npx
- **Build Tool**: esbuild or tsx
- **Testing**: Jest or Vitest

## Project Structure

```
src/
├── mcp/
│   ├── server.ts           # Main MCP server implementation
│   ├── tools/              # MCP tool definitions
│   │   ├── solver.ts       # Solver-specific tools
│   │   ├── matrix.ts       # Matrix operation tools
│   │   └── graph.ts        # Graph algorithm tools
│   ├── resources/          # MCP resource providers
│   │   ├── algorithms.ts   # Algorithm documentation resources
│   │   └── examples.ts     # Example problems and solutions
│   ├── prompts/            # MCP prompt templates
│   │   └── solver.ts       # Solver-specific prompts
│   └── index.ts           # Entry point for MCP server
├── cli/
│   └── index.ts           # CLI wrapper for npx execution
├── core/                   # Core solver implementations
│   ├── types.ts           # TypeScript type definitions
│   ├── matrix.ts          # Matrix operations
│   ├── solver.ts          # Main solver algorithms
│   └── utils.ts           # Utility functions
└── tests/
    ├── mcp/               # MCP-specific tests
    └── core/              # Core functionality tests
```

## Implementation Phases

### Phase 1: Core Setup (Week 1)

1. **Initialize TypeScript Project**
   - Set up package.json with npx configuration
   - Configure TypeScript with strict mode
   - Install FastMCP and dependencies
   - Set up build pipeline

2. **Define Core Types**
   - Matrix representation types
   - Solver configuration interfaces
   - Result types with error handling
   - MCP message types

3. **Basic MCP Server**
   - Create minimal FastMCP server
   - Implement health check endpoint
   - Set up logging and error handling
   - Test basic connectivity

### Phase 2: Solver Integration (Week 2)

1. **Implement Core Algorithms**
   - Port existing solver algorithms to TypeScript
   - Implement Neumann series expansion
   - Add random walk sampling
   - Implement forward/backward push methods

2. **Create MCP Tools**
   ```typescript
   // Example tool definitions
   - solveDiagonallyDominant: Solve ADD systems
   - estimateCoordinate: Estimate single coordinate
   - computePageRank: PageRank computation
   - analyzeConvergence: Check convergence properties
   ```

3. **Add Resource Providers**
   - Algorithm documentation
   - Performance benchmarks
   - Example matrices and solutions
   - Configuration templates

### Phase 3: Advanced Features (Week 3)

1. **Bidirectional Solver**
   - Implement forward-backward combination
   - Add optimization heuristics
   - Performance monitoring

2. **Streaming Support**
   - Add streaming for large matrix operations
   - Progress reporting for long-running computations
   - Incremental result updates

3. **Caching Layer**
   - Cache frequently accessed matrices
   - Memoize intermediate computations
   - Result caching with TTL

### Phase 4: CLI and Distribution (Week 4)

1. **CLI Implementation**
   - Command-line argument parsing
   - Interactive mode
   - Output formatting (JSON, CSV, etc.)
   - Progress indicators

2. **NPX Package Setup**
   ```json
   {
     "name": "sublinear-solver-mcp",
     "bin": {
       "sublinear-solver": "./dist/cli/index.js"
     },
     "scripts": {
       "start": "node dist/mcp/index.js"
     }
   }
   ```

3. **Documentation**
   - API documentation
   - Usage examples
   - Integration guides
   - Performance tuning guide

## MCP Tool Specifications

### Core Tools

1. **solve**
   ```typescript
   interface SolveParams {
     matrix: number[][] | SparseMatrix;
     vector: number[];
     method?: 'neumann' | 'random-walk' | 'push';
     epsilon?: number;
     maxIterations?: number;
   }
   ```

2. **estimateEntry**
   ```typescript
   interface EstimateEntryParams {
     matrix: number[][] | SparseMatrix;
     row: number;
     column: number;
     epsilon: number;
     confidence?: number;
   }
   ```

3. **analyzeMatrix**
   ```typescript
   interface AnalyzeMatrixParams {
     matrix: number[][] | SparseMatrix;
     checkDominance?: boolean;
     computeGap?: boolean;
     estimateCondition?: boolean;
   }
   ```

### Graph Tools

1. **pageRank**
   ```typescript
   interface PageRankParams {
     adjacency: number[][] | SparseMatrix;
     damping?: number;
     personalized?: number[];
     epsilon?: number;
   }
   ```

2. **effectiveResistance**
   ```typescript
   interface EffectiveResistanceParams {
     laplacian: number[][] | SparseMatrix;
     source: number;
     target: number;
     epsilon?: number;
   }
   ```

## FastMCP Integration

### Server Configuration

```typescript
import { FastMCP } from '@fastmcp/core';

const server = new FastMCP({
  name: 'sublinear-solver',
  version: '1.0.0',
  description: 'Sublinear-time solver for ADD systems'
});

// Register tools
server.tool('solve', solveTool);
server.tool('analyze', analyzeTool);

// Register resources
server.resource('algorithms/*', algorithmProvider);
server.resource('examples/*', exampleProvider);

// Register prompts
server.prompt('optimize', optimizationPrompt);
```

### Error Handling

```typescript
class SolverError extends Error {
  constructor(
    message: string,
    public code: string,
    public details?: any
  ) {
    super(message);
  }
}

// Error codes
const ErrorCodes = {
  NOT_DIAGONALLY_DOMINANT: 'E001',
  CONVERGENCE_FAILED: 'E002',
  INVALID_MATRIX: 'E003',
  TIMEOUT: 'E004'
};
```

## Performance Considerations

1. **Memory Management**
   - Use sparse matrix representations
   - Implement streaming for large datasets
   - Clear caches periodically

2. **Computation Optimization**
   - Use WebAssembly for critical paths
   - Implement parallel processing where possible
   - Adaptive algorithm selection based on matrix properties

3. **Network Efficiency**
   - Compress large matrix transfers
   - Use binary protocols for numerical data
   - Implement request batching

## Testing Strategy

1. **Unit Tests**
   - Core algorithm correctness
   - Edge cases (singular matrices, etc.)
   - Performance regression tests

2. **Integration Tests**
   - MCP protocol compliance
   - End-to-end solver workflows
   - Error handling scenarios

3. **Performance Tests**
   - Benchmark against reference implementations
   - Scalability testing with large matrices
   - Memory usage profiling

## Deployment

### NPX Distribution

```bash
# Users can run directly:
npx sublinear-solver-mcp serve

# Or install globally:
npm install -g sublinear-solver-mcp
sublinear-solver serve
```

### Docker Support

```dockerfile
FROM node:20-alpine
WORKDIR /app
COPY package*.json ./
RUN npm ci --only=production
COPY dist ./dist
EXPOSE 3000
CMD ["npm", "start"]
```

## Integration Examples

### With Claude Desktop

```json
{
  "mcpServers": {
    "sublinear-solver": {
      "command": "npx",
      "args": ["sublinear-solver-mcp", "serve"],
      "env": {
        "SOLVER_MAX_MEMORY": "2GB",
        "SOLVER_TIMEOUT": "30000"
      }
    }
  }
}
```

### Programmatic Usage

```typescript
import { SolverClient } from 'sublinear-solver-mcp';

const client = new SolverClient();
const result = await client.solve({
  matrix: [[4, -1, 0], [-1, 4, -1], [0, -1, 4]],
  vector: [1, 2, 1],
  epsilon: 0.001
});
```

## Success Metrics

1. **Performance**
   - Achieve sublinear time complexity for supported operations
   - Handle matrices up to 1M×1M sparse entries
   - Response time < 100ms for small matrices

2. **Reliability**
   - 99.9% uptime for MCP server
   - Graceful degradation for edge cases
   - Comprehensive error messages

3. **Adoption**
   - npm weekly downloads > 1000
   - GitHub stars > 100
   - Active community contributions

## Timeline

- **Week 1**: Core setup and basic MCP server
- **Week 2**: Algorithm implementation and tool creation
- **Week 3**: Advanced features and optimization
- **Week 4**: CLI, documentation, and release
- **Week 5**: Testing, bug fixes, and performance tuning
- **Week 6**: Release and community engagement

## Open Questions

1. Should we support GPU acceleration for large matrices?
2. What serialization format is optimal for sparse matrices?
3. Should we implement a web-based UI for visualization?
4. How to handle distributed computation for very large systems?
5. What telemetry/monitoring should be included?

## References

- [FastMCP Documentation](https://github.com/fastmcp/fastmcp)
- [MCP Specification](https://modelcontextprotocol.io)
- [Original Research Papers](../research.md)
- [TypeScript Best Practices](https://typescript.style)